Consider two individuals, Dave and Eva. Both Dave and Eva have initial wealth 810, 000 and face a 40% chance of losing L = 450, 000. Dave has von Neumann-Morgenstern utility function up(x) = x and Eva has von Neumann-Morgenstern utility function uf(x) = Vx. 1. What do you know about Dave's and Eva's risk preferences? 2. What is the most Dave would be willing to pay for complete insurance against the loss? 3. What is the most Eva would be willing to pay for complete insurance against the loss?
Consider two individuals, Dave and Eva. Both Dave and Eva have initial wealth 810, 000 and face a 40% chance of losing L = 450, 000. Dave has von Neumann-Morgenstern utility function up(x) = x and Eva has von Neumann-Morgenstern utility function uf(x) = Vx. 1. What do you know about Dave's and Eva's risk preferences? 2. What is the most Dave would be willing to pay for complete insurance against the loss? 3. What is the most Eva would be willing to pay for complete insurance against the loss?
Brief Principles of Macroeconomics (MindTap Course List)
8th Edition
ISBN:9781337091985
Author:N. Gregory Mankiw
Publisher:N. Gregory Mankiw
Chapter9: The Basic Tools Of Finance
Section: Chapter Questions
Problem 9PA
Related questions
Question
![Exercise 5: Insurance
Consider two individuals, Dave and Eva. Both Dave and Eva have initial wealth 810,000 and face a 40%
chance of losing L = 450, 000. Dave has von Neumann-Morgenstern utility function up(x)
= x and Eva has
von Neumann-Morgenstern utility function uf (x) = VT.
1. What do you know about Dave's and Eva's risk preferences?
2. What is the most Dave would be willing to pay for complete insurance against the loss?
3. What is the most Eva would be willing to pay for complete insurance against the loss?
Suppose they are each able to choose insurance with any coverage level z E [0, 1] (i.e. 0 < z < 1). If an
individual buys insurance coverage at level z, they will get reimbursed 450, 000 · z if the loss occurs. Insurance
coverage at level z costs ((z) = z ·
200, 000.
4. What coverage level 2, would Dave choose? Explain.
5. Based on your previous results, try to explain that Eva chooses a strictly positive coverage z > 0.
6. Is Eva's optimal choice full insurance, i.e. z = 1?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F984ca259-54f9-4683-afd9-6096ed5265a3%2F4b30ecc1-705c-47ab-b89d-764176e9fd5e%2Fyoe0m5a_processed.png&w=3840&q=75)
Transcribed Image Text:Exercise 5: Insurance
Consider two individuals, Dave and Eva. Both Dave and Eva have initial wealth 810,000 and face a 40%
chance of losing L = 450, 000. Dave has von Neumann-Morgenstern utility function up(x)
= x and Eva has
von Neumann-Morgenstern utility function uf (x) = VT.
1. What do you know about Dave's and Eva's risk preferences?
2. What is the most Dave would be willing to pay for complete insurance against the loss?
3. What is the most Eva would be willing to pay for complete insurance against the loss?
Suppose they are each able to choose insurance with any coverage level z E [0, 1] (i.e. 0 < z < 1). If an
individual buys insurance coverage at level z, they will get reimbursed 450, 000 · z if the loss occurs. Insurance
coverage at level z costs ((z) = z ·
200, 000.
4. What coverage level 2, would Dave choose? Explain.
5. Based on your previous results, try to explain that Eva chooses a strictly positive coverage z > 0.
6. Is Eva's optimal choice full insurance, i.e. z = 1?
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 5 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.Recommended textbooks for you
![Brief Principles of Macroeconomics (MindTap Cours…](https://www.bartleby.com/isbn_cover_images/9781337091985/9781337091985_smallCoverImage.gif)
Brief Principles of Macroeconomics (MindTap Cours…
Economics
ISBN:
9781337091985
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
![Essentials of Economics (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781337091992/9781337091992_smallCoverImage.gif)
Essentials of Economics (MindTap Course List)
Economics
ISBN:
9781337091992
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
![Brief Principles of Macroeconomics (MindTap Cours…](https://www.bartleby.com/isbn_cover_images/9781337091985/9781337091985_smallCoverImage.gif)
Brief Principles of Macroeconomics (MindTap Cours…
Economics
ISBN:
9781337091985
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
![Essentials of Economics (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781337091992/9781337091992_smallCoverImage.gif)
Essentials of Economics (MindTap Course List)
Economics
ISBN:
9781337091992
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning